Existence, uniqueness and finite element approximation of the solution of time-harmonic electromagnetic boundary value problems involving metamaterials

Existence and uniqueness of the solution of time-harmonic electromagnetic boundary value problems is analyzed together with the convergence of Galerkin finite element approximations. Sufficient conditions based on the presence of different types of losses and on the properties of the hermitian symmetric parts of the effective dielectric permittivity and the effective magnetic permeability are provided. Metamaterials such as double-negative, epsilon-negative and mu-negative substances are covered by our analysis since any hypothesis on the positive definiteness of the aforementioned hermitian symmetric parts is avoided on purpose. Index terms Metamaterials, double-negative materials, epsilon-negative materials, mu-negative materials, existence, uniqueness, finite element approximation, convergence.